Question

The value of tan^2 30 degree + 4sin^2 45 degree + cos^2 30 degree is

Answer 1

$The \: value \:of \: tan^{2} 30\degree + 4 sin^{2} 45\degree + cos^{2} 30\degree$

$= \Big( \frac{1}{\sqrt{3}}\Big)^{2} + 4 \Big(\frac{1}{\sqrt{2}}\Big)^{2} + \Big( \frac{\sqrt{3}}{2}\Big)^{2}$

$= \frac{1}{3} + 4 \times \frac{1}{2} + \frac{3}{4}$

$= \frac{1}{3} + 2 + \frac{3}{4}$

$= \frac{4+8+9}{12}$

$= \frac{21}{12}$

$= \frac{7}{4}$

Therefore.,

$\red{The \: value \:of \: tan^{2} 30\degree + 4 sin^{2} 45\degree + cos^{2} 30\degree}$

$\green { = \frac{7}{4}}$

•••♪

Answer 2

$\huge\bf\red{Question}$

The value of tan^2 30 degree + 4sin^2 45 degree + cos^2 30 degree is

$\huge \bf\orange{Solution}$

$\sf\mapsto\:\:\:\purple{\Big( \dfrac{1}{\sqrt{3}}\Big)^{2} + 4 \Big(\dfrac{1}{\sqrt{2}}\Big)^{2} + \Big( \dfrac{\sqrt{3}}{2}\Big)^{2} }$

$\sf\mapsto\:\:\:\green{ \dfrac{1}{3} + 4 \times \dfrac{1}{2} + \dfrac{3}{4}}$

$\sf\mapsto\:\:\:\purple{ \dfrac{1}{3} + 2 + \dfrac{3}{4}}$

$\sf\mapsto\:\:\:\green{\dfrac{4+8+9}{12}}$

$\sf\mapsto\:\:\:\purple{ \dfrac{\cancel{21}}{\cancel{12}} }$

$\sf\mapsto\:\:\:\green{ \dfrac{7}{4}}$

$\tt\red{\therefore\:\:The \: value \:of \: tan^{2} 30\degree + 4 sin^{2} 45\degree + cos^{2} 30\degree \ = \ \dfrac{7}{4}}$